Cardinal invariants of paratopological groups

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We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.

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@article{IvánSánchez2013, abstract = {We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.}, author = {Iván Sánchez}, journal = {Topological Algebra and its Applications}, keywords = {Paratopological group; Totally ω-narrow; Index of regularity; Weak Lindelöf number; Hausdorff number; Symmetry number; Regular Gσ-diagonal; paratopological group; semitopological group; cardinal invariant; totally narrow; index of regularity; weak Lindelöf number; symmetry number; regular -diagonal}, language = {eng}, pages = {37-45}, title = {Cardinal invariants of paratopological groups}, url = {http://eudml.org/doc/267157}, volume = {1}, year = {2013},}

TY - JOURAU - Iván SánchezTI - Cardinal invariants of paratopological groupsJO - Topological Algebra and its ApplicationsPY - 2013VL - 1SP - 37EP - 45AB - We show that a regular totally ω-narrow paratopological group G has countable index of regularity, i.e., for every neighborhood U of the identity e of G, we can find a neighborhood V of e and a countable family of neighborhoods of e in G such that ∩W∈γ VW−1⊆ U. We prove that every regular (Hausdorff) totally !-narrow paratopological group is completely regular (functionally Hausdorff). We show that the index of regularity of a regular paratopological group is less than or equal to the weak Lindelöf number. We also prove that every Hausdorff paratopological group with countable π- character has a regular Gσ-diagonal.LA - engKW - Paratopological group; Totally ω-narrow; Index of regularity; Weak Lindelöf number; Hausdorff number; Symmetry number; Regular Gσ-diagonal; paratopological group; semitopological group; cardinal invariant; totally narrow; index of regularity; weak Lindelöf number; symmetry number; regular -diagonalUR - http://eudml.org/doc/267157ER -